Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Skill Practice - Page 892: 25

$$A=4\sqrt{39}$$

By Heron's Formula, we know: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ Where: $$s=\frac{a+b+c}{2}$$ Thus, we find: $$s=\frac{5+11+10}{2}=13 \\ A=\sqrt{13\left(13-5\right)\left(13-11\right)\left(13-10\right)} \\ A=4\sqrt{39}$$